Mathematical models that generate scenarios containing no temporal correspondence to time series of actual occurrences are difficult to evaluate. One such class of models consists of atmospheric General Circulation Models (GCM), which have an additional drawback that the temporal and spatial scales of their outputs do not match those of the actual observations of the simulated phenomena. The problem of disparate scales can be ameliorated by aggregating both the model output and the observed data to commensurate scales. However, this approach does not permit quantitative testing at scales less than the least common level of aggregation. The lack of paired observations in the aggregated time series makes standard statistical methods either invalid or ineffective in testing the validity of a GCM. One approach to resolving this quandary is the use of a relative information measure, which is based on the uncertainties contained in the histograms of the aggregations of both the model output and the data base. Each interval of each histogram is analyzed, from a Bayesian perspective, as a binomial probability. For the data-based histogram, the reciprocal of the sum of the variances of the posterior distributions of probability in each interval is denoted as its information content. For the model-based histogram, the reciprocal of the sum of the expected mean squared errors of the posterior distributions in each interval likewise is its information content. The expected mean squared error, which accounts for potential biases in the GCM, is computed as the expectation of the squared differences between the data-based and the model-based posterior distributions for each interval. The ratio of the information content of the model-based histogram to that of the data-based histogram is the relative information of the model. A 5-year monthly precipitation time series for January at a single node of the current version of the Community Climate Model including the Biosphere Atmosphere Transfer Scheme contains 7.5% of the information in the most recent 30 years of data in the Climatological Data Set assembled by the National Climate Data Center (NCDC). If the 5-year simulation were extended, its relative information content could be expected to approach 11.5%.

For July monthly precipitation, the 5-year simulation contained 13.7% of the information of the NCDC data base and had a limit of 39.3% for extremely long simulations. Aggregation of two adjacent cells at the same latitude showed some improvements in relative information, but longitudinal aggregation with two additional adjacent cells showed improvement for January precipitation, but degraded information for July precipitation.